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21 June 2008

1st Day Issue / Tierra de los Sueños / cannonball dropped from Tower of Pisa / Baseball dropped from Washington Monument

Click image for larger.

See previous PizzaQ post. This image has everything you need to solve the PizzaQ. Answers should have 3 digits of precision to the right of the decimal point.

The constant of acceleration -- g -- due to gravity is defined for Earth Sea Level.

For the purposes of this question, Pisa and Washington DC are Vacuum Zones, they have no air or atmosphere, and thus objects fall without air resistance.

3 comments:

abbas halai said...

i tried to post this last night but blogger ate my comment.

well g on earth at sea level.

let's see

Fg = G * (m1.m2)/r^2

which basically means that force of gravity between any two objects is inversely proportional to the square of the distance between them.

where G is the universal Gravitational Constant, m1 is the mass of the first object, m2 is the mass of the second object and r is the distance between the two objects and Fg is the force of Gravity between the two objects.

so....let's see...

r is the radius of the earth which averages at 6,372,797 m

m1 is me at 60 kg

m2 is the mass of the earth at 5.9742 × 10^24 kg

and G is 6.67300 × 10^-11 m^3 kg^-1 s^-2

so Fg = (6.67300 * 10^-11) * [60*(5.9742 * 10^24)]/(6372797 * 6372797)

therefor Fg = 589 N

From Newton's second law, this roughly equates to F = m.a since my mass is negligible compared to the rest of the planet's.

If my force is 589 N and my mass is 60kg, the acceleration due to gravity is 9.8 m/s^2.

Vleeptron Dude said...

This must be my fault somehow.

I just wanna know how long it takes the cannonball to fall from the top of the Pisa Tower to the ground.

& for the extra slice, how long it takes the baseball to fall from the top of the Washington Monument to the ground.

So it's much simpler than you're making it. Just use the equation above:

t = sqr[ 2s / g ]

That Sea Level thing ... well, you're right, of course, the force of gravity pulling objects toward the center of the Earth diminishes (by the law of inverse squares) with the object's distance from the center of the Earth.

But for all practical object falling problems on the surface of the Earth, it pretty much doesn't matter. The attraction changes by such a tiny amount from the top to the bottom of the drop, even if top is Mount Everest. Just use g as defined in the illustration. (i.e., treat g as a constant, not as a variable.)

So how many seconds does it take for the cannonball to hit the ground; ditto the baseball?

Because you're the only person to take a whack at this, here's another pizza slice for Your Great City Building. How long does it take a hockey puck to fall from the top of CN Tower?

=========

The CN Tower, located in downtown Toronto, Ontario, Canada, is a communications and tourist tower standing 553.33 metres (1,815.39 ft) tall. It surpassed the height of the Ostankino Tower while still under construction in 1975, becoming the tallest free-standing structure on land in the world.

On September 12, 2007, after holding the record for 31 years, the CN tower was surpassed in height by the still-under-construction Burj Dubai.

Vleeptron Dude said...

MEANWHILE ...

Back to Galileo's original experiment, which disproved Aristotle's contention that heavier objects fall faster than lighter objects.

And that annoying Air stuff which distorts the experiment with Air Resistance when you try to do it on Earth.

So here's a video of an astronaut finally putting the question to rest by simultaneously dropping a hammer and a feather from neck-high to the surface of the Moon:

http://radicalfilms.co.uk/2008/01/26/hammer-and-feather-dropped-on-moon-by-apollo-15-astronaut-dave-scott/

As you'll see from the accompanying text and comments, this film is also used to prove that human beings really did get to the Moon, and it wasn't all a hoax in a Hollywood studio.

(Of course Hollywood COULD have built the studio inside a vacuum.)